Order of element

Printable View

November 4th 2009, 03:54 PM
apple2009

Order of element

Let G be a finite group. Prove the order of any element v (which v is an element of G) divides the order |G|of G.
November 4th 2009, 03:59 PM
Drexel28

Quote:

Originally Posted by apple2009

Let G be a finite group. Prove the order of any element v (which v is an element of G) divides the order |G|of G.

Hint: $\langle v\rangle$ is a subgroup of $G$ . Now apply Lagrange's theorem.
November 4th 2009, 04:04 PM
apple2009

am I need to prove v is a subgroup of G? and how?
November 4th 2009, 04:10 PM
Drexel28

Quote:

Originally Posted by apple2009

am I need to prove v is a subgroup of G? and how?

You already know that $\langle v\rangle$ is a subgroup of $G$ (or you should). Now use the fact that $|v|=|\langle v\rangle|$ and Lagranges theorem.

All times are GMT -8. The time now is 01:29 PM.